Problem: The sum of two numbers is $79$, and their difference is $5$. What are the two numbers?
Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 79}$ ${x-y = 5}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 84 $ $ x = \dfrac{84}{2} $ ${x = 42}$ Now that you know ${x = 42}$ , plug it back into $ {x+y = 79}$ to find $y$ ${(42)}{ + y = 79}$ ${y = 37}$ You can also plug ${x = 42}$ into $ {x-y = 5}$ and get the same answer for $y$ ${(42)}{ - y = 5}$ ${y = 37}$ Therefore, the larger number is $42$, and the smaller number is $37$.